On the reconstruction of inclusions in a heat conductive body from dynamical boundary data over a finite time interval

Abstract

The enclosure method was originally introduced for inverse problems concerning non-destructive evaluation governed by elliptic equations. It was developed as one of the useful approaches in inverse problems and applied for various equations. In this paper, an application of the enclosure method to an inverse initial boundary value problem for a parabolic equation with a discontinuous coefficient is given. A simple method to extract the depth of unknown inclusions in a heat conductive body from a single set of the temperature and heat flux on the boundary observed over a finite time interval is introduced. Other related results with infinitely many data are also reported. One of them gives the minimum radius of the open ball centred at a given point that contains the inclusions. The formula for the minimum radius is newly discovered.